Optical scanning apparatus and image-forming apparatus

ABSTRACT

An optical scanning apparatus includes a light-source unit, an incident optical system for directing light beams emitted from the light-source unit to a deflecting unit, and an imaging optical system for guiding the light beams deflected from the deflecting unit to a surface to be scanned. The imaging optical system includes a toric lens whose power in the main scanning direction is different from that in the sub-scanning direction; the toric lens having the curvature centers of the meridians of a first toric surface connected to form a curved line located in a common plane Ha, and the curvature centers of the meridians of a second toric surface connected to form a curved line not located in a common plane.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.11/432,211 filed May 10, 2006, now U.S. Pat. No. 7,551,338, which claimspriority to Japanese Patent Application No. 2005-153931 filed May 26,2005, both of which are hereby incorporated by reference herein in theirentirety.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to an optical scanning apparatus and animage-forming apparatus using the same.

2. Description of the Related Art

To date, in an optical scanning apparatus, light beams modulated andemitted from a light-source unit are periodically deflected by a lightdeflector according to image signals, and converged on a plane of aphotosensitive recording medium as a spot by an imaging optical systemhaving an fθ characteristic such that images are recorded on the plane.

Recently, such imaging optical systems have been required to be fasterand more compact as apparatuses such as laser-beam printers, digitalcopiers, and multifunctional printers increase in speed and decrease insize.

As one measure for enhancing the speed, an overfilled optical system(OFS) has been used. In the OFS, the width of incoming beams incident ona deflection plane of a light deflector (rotatable polygon mirror) islarger than the width of the deflection plane in a main scanningsection. Accordingly, the diameter of the light deflector can be smalland the number of planes thereof can be increased, and thus the speed ofthe light deflector can be enhanced.

According to this feature of the OFS, the incoming beams incident on thedeflection plane of the light deflector and scanning beams deflectedfrom the deflection plane and reaching a surface to be scanned arerequired to be spatially separated in a sub-scanning section.

Also, when a plurality of light beams are deflected from an identicaldeflection plane of a light deflector and individually emitted to aplurality of planes to be scanned in an underfilled optical system(UFS), the plurality of light beams are required to be spatiallyseparated in the sub-scanning section after the deflection.

In order to spatially separate the light beams, for example, thedirection of the incoming beams incident on the deflection plane of thelight deflector is inclined with respect to the deflection plane in thesub-scanning section.

When the optical structure of the optical scanning apparatus becomescompact, the length of the optical path for spatial separation becomesshort. Therefore, the inclination of the incoming beams incident on thedeflection plane of the light deflector defined in the sub-scanningsection is required to be larger with respect to the deflection plane.Moreover, the maximum scanning angle is required to be larger such thatthe length of the optical path from the deflection plane of the lightdeflector to the surface of a photosensitive drum (the surface to bescanned) is reduced.

However, when the inclination of the incoming beams and the scanningangle are increased as described above, the light beams obliquelyincident on the deflection plane of the light deflector in thesub-scanning section draw a conical plane due to the deflection scanningof the light deflector (conical scan), resulting in the following twomajor problems.

A first problem is that the light beams obliquely incident on thedeflection plane of the light deflector in the sub-scanning section drawa conical plane due to the deflection scanning of the light deflector,and thus, the curved scanning beams are incident on an fθ lens (imaginglens) disposed in the center of the oblique incoming beams such that acurved scanning line also appears on the surface of the photosensitivedrum serving as the surface to be scanned. This is the problem of thecurvature of the scanning line caused by the incoming beams obliquelyincident on the deflection plane of the light deflector in thesub-scanning section.

A second problem is deterioration in imaging performance since thescanning beams that are deflected from the deflection plane and reachthe surface to be scanned draw a conical plane. When the main scanningdirection in the incident optical system can be defined as a mainscanning direction of the light beams, the angle of the deflected lightbeams inclined with respect to generatrices (main scanning direction) ofthe fθ lens in the main scanning direction is increased with thescanning angle. That is to say, since directions (main scanningdirection and sub-scanning direction) of refracting power to be given tothe light beams by the lens surfaces are deviated (rotated) in areaswith large scanning angles, the shape of the spot on the surface of thephotosensitive drum is distorted to form, for example, a star shape.This is the problem of the deterioration in the imaging performancecaused by the scanning beams drawing a conical plane.

When an optical scanning apparatus having the two problems describedabove is used for an image-forming apparatus, formed images areconsiderably deteriorated.

To date, various optical scanning apparatuses for solving these twoproblems have been discussed (for example, U.S. Pat. No. 6,141,118).

In U.S. Pat. No. 6,141,118, the optical axis of a toric lens used in animaging optical system and light beams deflected by a light deflectorare disposed collinear with respect to each other in the sub-scanningsection, and both surfaces of the toric lens are formed such thatgeneratrices formed by connecting the vertexes of meridians of each lenssurface are curved in the sub-scanning direction. In this manner, thedeterioration in the imaging performance and the curvature of thescanning line are corrected.

In this method, the generatrices of both the lens surfaces of the toriclens curved in the sub-scanning direction produce an effect equal to acase where a cylindrical lens having power in the sub-scanning directionis rotated around the optical axis of the toric lens. By action of thiseffect of rotating the cylindrical lens around the optical axis of thetoric lens, the influence of deviation (rotation) in the directions(main scanning direction and sub-scanning direction) of the refractingpower to be given by the lens surfaces to the light beams deflected bythe conical scan is cancelled, and the deterioration in the imagingperformance is corrected or error reduced.

However, when the lens surfaces of the toric lens are formed such thatthe generatrices are curved in the sub-scanning direction, the shapes ofthe lens surfaces become complicated. Therefore, the lens surface havinga high degree of effectiveness of reduction in the deterioration in theimaging performance can be formed such that the generatrix is curved inthe sub-scanning direction.

Moreover, in U.S. Pat. No. 6,141,118, the optical axis of the toric lensof the imaging optical system is inclined with respect to the incomingbeams that are incident on the incident plane of the toric lens in thesub-scanning section such that the deterioration in the imagingperformance and the curvature of the scanning line are regulated.However, when the maximum scanning angle (maximum angle of view) or theinclination of the incoming beams incident on the deflection plane ofthe light deflector with respect to the deflection plane defined in thesub-scanning section is large in the imaging optical system, thedeterioration in the imaging performance and the curvature of thescanning line on the surface to be scanned over the entire range ofimage heights are difficult to sufficiently regulate by changing theinclination of the toric lens in the sub-scanning section.

SUMMARY OF THE INVENTION

At least one exemplary embodiment is directed to an optical scanningapparatus used in image-forming apparatuses (e.g., laser-beam printers,digital copiers, and multifunctional printers) that performelectrophotographic processes.

The present invention is directed to optical scanning apparatusescapable of correcting deterioration in imaging performance and curvatureof a scanning line on a surface to be scanned and capable of forminghigh-definition and high-resolution images, and provides image-formingapparatuses using the same.

An optical scanning apparatus includes a light-source unit, an incidentoptical system for directing light beams emitted from the light-sourceunit to a deflecting unit, and an imaging optical system for guiding thelight beams deflected from the deflecting unit to a surface to bescanned. The imaging optical system includes a toric lens whose power inthe main scanning direction is different from that in the sub-scanningdirection; the toric lens, which can have the curvature centers of themeridians of a first toric surface connected to form a curved linelocated in a common plane Ha, and the curvature centers of the meridiansof a second toric surface connected to form a curved line not located ina common plane.

The optical scanning apparatus includes curvature radii of the meridiansof the first toric surface of the toric lens that vary in magnitude fromthe optical axis of the imaging optical system toward the periphery.

The optical scanning apparatus includes the plane Ha which is notparallel to principal rays of incoming beams incident on the toric lenstraveling toward the central image height of the surface to be scannedin the sub-scanning section.

The optical scanning apparatus includes the first toric surface of thetoric lens that has areas that satisfy the following condition:100≦|Ra|(mm),

where Ra indicates the curvature radii of the meridians.

The optical scanning apparatus includes the condition where thedirection of the light beams emitted from the light-source unit andentering a deflection plane of the deflecting unit is inclined withrespect to the deflection plane in the sub-scanning section in theincident optical system.

The optical scanning apparatus includes the condition where the degreeof curvature ΔA of a generatrix of the second toric surface satisfiesthe following conditions:0≦ΔA≦1(mm)ΔA=|Zmax−Zmin| (mm),

where Zmax and Zmin indicate the maximum value and the minimum value,respectively, of the central positions of the curvature radii of themeridians of the second toric surface in the Z direction when the pointof intersection of the optical axis of the second toric surface and thecurved surface of the lens is defined as the origin, and an axisorthogonal to the optical axis in the sub-scanning section is defined asthe Z axis.

The optical scanning apparatus includes the imaging optical system thatincludes a single toric lens.

The optical scanning apparatus includes the generatrix of the secondtoric surface of the toric lens formed by connecting the vertexes of themeridians in every area of the second toric surface is curved in thesub-scanning direction.

The optical scanning apparatus includes the condition where thecurvature radii of the meridians of both the first toric surface and thesecond toric surface of the toric lens vary in magnitude from theoptical axis of the imaging optical system toward the periphery.

An image-forming apparatus includes the optical scanning apparatusdescribed above, a photosensitive member disposed on a surface to bescanned, a developing unit for developing electrostatic latent images onthe photosensitive member as toner images, the electrostatic latentimages being formed by the light beams that are emitted by the opticalscanning apparatus and scan the photosensitive member, a transferringunit for transferring the developed toner images to a recordingmaterial, and a fixing unit for fixing the transferred toner images onthe recording material.

An image-forming apparatus includes the optical scanning apparatusdescribed above, and a printer controller converting code data input byan external apparatus into image signals and sending the signals to theoptical scanning apparatus.

A color-image forming apparatus includes a plurality of optical scanningapparatuses described above, and a plurality of image carriers disposedon planes to be scanned of the optical scanning apparatuses and eachforming images of a corresponding color.

The color-image forming apparatus includes a printer controllerconverting color signals input by an external apparatus into image dataof different colors and sending pieces of the data to the respectiveoptical scanning apparatuses.

According to an aspect of the present invention, optical scanningapparatuses capable of forming high-definition and high-resolutionimages and image-forming apparatuses using the same can be realized byforming a simplified toric lens of an imaging optical system such thatdeterioration in imaging performance and curvature of a scanning line ona surface to be scanned are corrected.

Further features of the present invention will become apparent from thefollowing description of exemplary embodiments with reference to theattached drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A is a schematic of a main scanning section according to a firstexemplary embodiment of the present invention, and FIG. 1B is aschematic of a sub-scanning section according to the first exemplaryembodiment of the present invention.

FIG. 2 illustrates the curvature radii of the meridians of an fθ lensaccording to the first exemplary embodiment of the present invention.

FIG. 3 illustrates curvatures of generatrices according to the firstexemplary embodiment of the present invention.

FIG. 4 illustrates the shapes of a spot at various image heightsaccording to the first exemplary embodiment of the present invention.

FIG. 5 illustrates the curvature of a scanning line according to thefirst exemplary embodiment of the present invention.

FIG. 6 illustrates the shape of a lens surface of a toric lens accordingto the first exemplary embodiment of the present invention.

FIG. 7 is a schematic of a sub-scanning section of an image-formingapparatus according to an exemplary embodiment of the present invention.

FIG. 8 is a schematic view of principal parts of a color-image formingapparatus according to an exemplary embodiment of the present invention.

DESCRIPTION OF THE EMBODIMENTS

The following description of at least one exemplary embodiment is merelyillustrative in nature and is in no way intended to limit the invention,its application, or uses.

Processes, techniques, apparatus, and materials as known by one ofordinary skill in the relevant art may not be discussed in detail butare intended to be part of the enabling description where appropriate,for example the fabrication of the lens elements and their materials.

In all of the examples illustrated and discussed herein any specificvalues, for example radius of curvatures, should be interpreted to beillustrative only and non limiting. Thus, other examples of theexemplary embodiments could have different values.

Notice that similar reference numerals and letters refer to similaritems in the following figures, and thus once an item is defined in onefigure, it may not be discussed for following figures.

Exemplary embodiments of the present invention will now be describedwith reference to the drawings.

First Exemplary Embodiment

FIG. 1A is a cross-sectional view of principal parts in the mainscanning direction (main scanning section) according to a firstexemplary embodiment of the present invention, and FIG. 1B is across-sectional view of the principal parts in the sub-scanningdirection (sub-scanning section) according to the first exemplaryembodiment of the present invention.

Herein, the main scanning direction is a direction perpendicular to therotation axis of a light deflector and the optical axis of an imagingoptical system (the direction in which light beams are deflected by thelight deflector). Herein, the sub-scanning direction is a directionparallel to the rotation axis of the light deflector. Moreover, the mainscanning section is a plane parallel to the main scanning directionincluding the optical axis of the imaging optical system. Furthermore,the sub-scanning section is a section perpendicular to the main scanningsection.

In the drawings, a light-source unit 1 can include a multibeammonolithic semiconductor laser having two luminous points. In thisexemplary embodiment, the number of the luminous points is two, but atleast one exemplary embodiment is not limited to this and the number canbe three or more, or one.

A cylindrical lens 2, which can have a predetermined power only in thesub-scanning direction, focuses incoming beams on a deflection plane(reflection plane) 6 a of a light deflector 6 described below in thesub-scanning section so as to form line images.

An aperture 3 regulates passing beams and adjusts the shape of thebeams.

A spherical lens (focusing lens) 4 converts the state of the light beamsregulated by the aperture 3 into a different state.

The cylindrical lens 2 and the spherical lens 4 can be one opticalelement.

A reflecting mirror 10 reflects the light beams passing through thespherical lens 4 toward the light deflector 6.

An incident optical system 5 includes components such as the cylindricallens 2, the aperture 3, the spherical lens 4, and the reflecting mirror10.

In this exemplary embodiment, the width of the light beams emitted fromthe light-source unit 1 and entering the deflection plane 6 a is madelarger than the width of the deflection plane 6 a of the light deflector6 in the main scanning section by the incident optical system 5(overfilled optical system; OFS).

The light deflector 6 can function as a deflecting unit, and can beformed of a rotatable polygon mirror. The light deflector 6 is rotatedin a direction of an arrow A in the drawings at a constant speed by adriving unit such as a motor (not shown).

An imaging optical system 18 has a light-condensing function and an fθcharacteristic, and includes a single toric lens (fθ lens) 8 whichincludes a resin material whose power in the main scanning direction isdifferent from that in the sub-scanning direction. The imaging opticalsystem 18 focuses the light beams, formed on the basis of imageinformation, deflected by the light deflector 6 on a surface of aphotosensitive drum 9 serving as a surface to be scanned in the mainscanning section so as to form a spot. Furthermore, the deflection plane6 a of the light deflector 6 and the surface of the photosensitive drum9 are optically conjugate in the sub-scanning section forsurface-tilting correction.

According to the toric lens 8 in this exemplary embodiment, thecurvature centers of the meridians of a second lens surface (emittingplane) R2 connected to form a curved line are not located in anidentical plane (i.e. common plane), and the curvature centers of themeridians of a first lens surface (incident plane) R1 connected to forma curved line are located in an identical plane (i.e. common plane) Ha.Furthermore, the first lens surface R1 is toric and the curvature radiiof the meridians vary depending on the positions of the radii in themain scanning direction. That is to say, the curvature radii of themeridians of the first lens surface R1 vary in magnitude from theoptical axis of the imaging optical system (center of the toric surface)toward the periphery.

The surface of the photosensitive drum 9 serves as a surface to bescanned, and a focused spot scans the surface of the photosensitive drum9 in the main scanning direction with a constant velocity.

In this exemplary embodiment, two light beams emitted from thelight-source unit 1 are converted into divergent beams in the mainscanning section and converted into slightly divergent beams in thesub-scanning section by the cylindrical lens 2. The beams then passthrough the aperture 3 (part of each of the beams is shielded by theaperture 3) and enter the spherical lens 4. The spherical lens 4converts the incoming beams into slightly convergent beams in the mainscanning section. The slightly convergent beams enter the deflectionplane 6 a from the center of the deflection angle (scanning angle) ofthe deflection plane 6 a of the light deflector 6 (center of thescanning range on the surface to be scanned) via the reflecting mirror10 (frontal incidence). The width of the incoming beams incident on thedeflection plane 6 a at this time is sufficiently wide with respect to afacet width of the deflection plane 6 a of the light deflector 6 in themain scanning section (OFS). On the other hand, the incoming beams arefocused on the deflection plane 6 a of the light deflector 6 so as toform line images (extending in the main scanning direction) in thesub-scanning section. At this time, the incoming beams are obliquelyincident on the deflection plane 6 a at a predetermined angle withrespect to a plane perpendicular to the rotation axis of the lightdeflector 6 (a rotational plane of the light deflector 6) in thesub-scanning section including the rotation axis of the light deflector6 and the optical axis of the imaging optical system 18(oblique-incidence optical system). That is to say, principal rays ofthe light beams incident on the deflection plane 6 a are inclined withrespect to the deflection plane 6 a in the sub-scanning section.

The two light beams deflected from the deflection plane 6 a of the lightdeflector 6 are then guided to the surface of the photosensitive drum 9via the toric lens 8, and the light beams scan the surface of thephotosensitive drum 9 in a direction of an arrow B (main scanningdirection) by rotating the light deflector 6 in the direction of thearrow A. In this manner, images are recorded on the surface of thephotosensitive drum 9 serving as a recording medium.

In this exemplary embodiment, the maximum scanning angle is set to awide angle of ±40.5° and the length Ld of an optical path from thedeflection plane 6 a of the light deflector 6 to the surface of thephotosensitive drum 9 is reduced such that the entire optical scanningapparatus becomes compact. Moreover, in this exemplary embodiment, theincoming beams incident on the deflection plane 6 a are inclined withrespect to the deflection plane 6 a at a predetermined angle (3° in thisexemplary embodiment) in the sub-scanning section such that the scanningbeams deflected from the deflection plane 6 a of the light deflector 6can be easily spatially separated in the sub-scanning section.

Moreover, in this exemplary embodiment, the imaging optical system 18includes only one toric lens 8 for simplicity (cost reduction).Furthermore, in order to ensure adequate fθ performance over the widescanning angle with only one toric lens 8, the generatrices of the toriclens 8 in the main scanning direction defined in the main scanningsection are non-arc shaped (gull-wing shaped) having inflection pointsas illustrated in FIG. 1A.

Since the generatrices of the toric lens 8 in the main scanningdirection have the inflection points as described above, positions ofprincipal points in the meridian direction (sub-scanning direction) arerequired to be actively changed according to image heights bycontinuously changing the curvature radii of the meridians of the firstlens surface (incident plane) R1 and the second lens surface (emittingplane) R2 of the toric lens 8 with respect to the main scanningdirection such that uniformity in magnification in the sub-scanningdirection is ensured.

Therefore, in this exemplary embodiment, the curvature radii R of themeridians of both the first lens surface R1 and the second lens surfaceR2 of the toric lens 8 are continuously changed with respect to the mainscanning direction as illustrated in FIG. 2 such that uniformity inmagnification in the sub-scanning direction is ensured. That is to say,the curvature radii R of the meridians of both the first lens surface(toric surface) R1 and the second lens surface (toric surface) R2 varyin magnitude from the optical axis of the imaging optical system (centerof the toric surfaces) toward the periphery.

FIG. 2 illustrates the curvature radii R of the meridians of the firstlens surface (toric surface) R1 and the second lens surface (toricsurface) R2 of the toric lens 8 according to this exemplary embodimentwith respect to the main scanning direction at positions from thecenters of the toric surfaces (the optical axis of the imaging opticalsystem).

In FIG. 2, the curvature centers of the meridians of the first lenssurface R1 connected to form a curved line are located in the identicalplane (i.e. common plane) Ha, and the curvature centers of the meridiansof the second lens surface R2 connected to form a curved line are notlocated in an identical plane (i.e. common plane). The generatrix of thesecond lens surface R2 formed by connecting the vertexes of themeridians in every area of the second lens surface R2 is curved in thesub-scanning direction. However, according to at least one exemplaryembodiment, the curvature centers of the meridians of the second lenssurface R2 connected to form a curved line can be located in theidentical plane (i.e. common plane) Ha, and the curvature centers of themeridians of the first lens surface R1 connected to form a curved linecan not be located in an identical plane (i.e. common plane).

As is clear from FIG. 2, the curvature radii R of the meridians of thesecond lens surface (toric surface) R2 in the outer portion of the toricsurface (remote from the optical axis of the imaging optical system) arelarger than those in the central portion (adjacent to the optical axisof the imaging optical system). The curvature radii R of the meridiansare in the following range:22 <R<−11 (mm)Thus, the curvature radii R of the meridians are sufficiently small overthe entire area of the lens of use and an effect of the curvature of thegeneratrix can be expected.

On the other hand, the curvature radii R of the meridians of the firstlens surface (toric surface) R1 in the outer portion (remote from theoptical axis of the imaging optical system) are larger than those in thecentral portion (adjacent to the optical axis of the imaging opticalsystem), and the curvature radii R of the meridians at ends are set to alarge value of approximately −172 mm.

In FIG. 2, areas Da1 and Da2 of the first lens surface R1 satisfy thefollowing condition:100≦|Ra|(mm)

where Ra indicates the curvature radii of the meridians in the mainscanning direction.

Power 1/Ra in the meridian direction is small at positions where thecurvature radii Ra of the meridians of the first lens surface R1adjacent to the ends are large. Therefore, an effect of rotating thetoric lens 8 around the optical axis is little, and thus an effect ofcancelling influences caused by the deviation (rotation) of thedirections (main scanning direction and sub-scanning direction) of therefracting power to be given to the deflected light beams by the lenssurface is little even when the generatrix is acutely curved in thesub-scanning direction.

Therefore, in this exemplary embodiment, the generatrix of the secondlens surface R2 of the toric lens 8 is curved in the sub-scanningdirection (the curvature centers of the meridians of the second lenssurface R2 connected to form a curved line are not located in anidentical plane (i.e. common plane)) since the effect of the curvatureof the generatrix of the second lens surface R2 in the sub-scanningdirection can be expected, and the generatrix of the first lens surfaceR1 is not curved in the sub-scanning direction (the curvature centers ofthe meridians of the first lens surface R1 connected to form a curvedline are located in the identical plane (i.e. common plane) Ha) suchthat the deterioration in the imaging performance is effectivelyreduced.

Moreover, in this exemplary embodiment, the plane Ha in which thecurvature centers of the meridians of the first lens surface R1 of thetoric lens 8 are located is not parallel to the principal rays of theincoming beams incident on the toric lens 8 propagating toward thecentral image height (a height of an intersection of the optical axisand the surface to be scanned) of the surface of the photosensitive drum9 as illustrated in FIG. 1B. Specifically, the toric lens 8 is inclinedby 5° in the sub-scanning section such that the first lens surface R1can also produce an effect of cancelling influences caused by thedeviation (rotation) of the directions (main scanning direction andsub-scanning direction) of the refracting power to be given to thedeflected light beams by the lens surface.

In this manner, the deterioration in the imaging performance and thecurvature of the scanning line can be appropriately corrected even ifthe curvature of the generatrix of the first lens surface R1 in thesub-scanning direction produces no effect. Moreover, lens warpage causedby the large curvature of the generatrix generated during fabrication ofthe lens can be regulated since the curvature of the generatrix of thesecond lens surface R2 in the sub-scanning direction, the curvaturebeing required to correct and/or reduce the deterioration in the imagingperformance and the curvature of the scanning line, can be small. Thus,the lens fabrication is facilitated.

FIG. 3 illustrates the shapes of the generatrices of the first lenssurface R1 and the second lens surface R2 of the toric lens 8 accordingto this exemplary embodiment. As is clear from FIG. 3, the generatrix ofthe second lens surface R2 is curved in the Z direction, and the degreeof the curvature ΔA is 30 μm, which is sufficiently small and causes notrouble in fabrication of the lens.

When the point of intersection of the optical axis and the curved secondlens surface R2 is defined as the origin and the axis orthogonal to theoptical axis in the sub-scanning section is defined as the Z axis (aside adjacent to the deflection point of the deflecting unit isnegative), the Z coordinate in FIG. 3 indicates the height of thecentral positions of the curvature radii of the meridians of the secondlens surface R2 in the Z direction. Accordingly, the degree of thecurvature AA of the generatrix of the second lens surface R2 in the Zdirection in FIG. 3 can be represented by the following expression:ΔA=|Zmax−Zmin|(mm),

where Zmax and Zmin indicate the maximum value and the minimum value,respectively, of the central positions of the curvature radii of themeridians of the toric surface in the Z direction. Since Zmax is 0.03 mmand Zmin is 0 mm in the second lens surface R2, the degree of thecurvature AA of the generatrix of the second lens surface R2 in the Zdirection is 0.03 mm. At this time, the degree of the curvature ΔAsatisfies the following condition:0≦ΔA≦1 (mm).When this conditional expression (b) is satisfied, the lens warpagecaused by the large curvature of the generatrix generated duringfabrication of the lens can be regulated. Moreover, in this exemplaryembodiment, the Z coordinate of the generatrix of the second lenssurface R2 in the outer portion of the lens is larger than that in thecentral portion in the main scanning direction (the side adjacent to thedeflection point of the deflecting unit is negative) such that rotationof the spot and the curvature of the scanning line caused by the conicalscan are regulated.

FIG. 4 illustrates the shapes of the focused spot at the image heights Yof −107, −100, −90, −53.5, and 0 according to this exemplary embodiment.As is clear from FIG. 4, the shape of the focused spot is appropriate atall the image heights.

FIG. 5 illustrates the curvatures of the scanning line on the surface ofthe photosensitive drum according to this exemplary embodiment. As isclear from FIG. 5, the curvature of the scanning line is regulated to 30μm or lower in a range of an effective scanning area of ±107 mm, whichis one pixel or lower with respect to a scanning-line density of 600 dpi(resolution of 42.3 μm), and thus sufficient optical performance isensured.

In this exemplary embodiment, the inclination of the toric lens 8 in thesub-scanning section and the curvature of the generatrix with respect tothe sub-scanning direction are both utilized. Accordingly, even when themaximum scanning angle (maximum angle of view) or the inclination of theincoming beams incident on the deflection plane of the light deflectorwith respect to the deflection plane defined in the sub-scanning sectionis large, and thus the deterioration in the imaging performance and thecurvature of the scanning line caused by the conical scan are large,these can be reduced so as to be negligible.

In this exemplary embodiment, the curvature radii of the meridians ofboth the first lens surface R1 and the second lens surface R2 of thetoric lens 8 vary with respect to the main scanning direction such thatuniformity in magnification in the sub-scanning direction is ensuredwith consideration of the shape of the generatrix of the toric lens 8 inthe main scanning direction. However, at least one exemplary embodimentis not limited to those described above, and, for example, the curvatureradii of the meridians can be constant in at least one exemplaryembodiment uniformity in magnification in the sub-scanning direction issufficiently ensured.

Moreover, in this exemplary embodiment, the optical axis of the toriclens 8 is inclined with respect to the principal rays of scanning beamsin the sub-scanning section. However, at least one exemplary embodimentis not limited to this, and, for example, the optical axis of the toriclens 8 can not be inclined with respect to the principal rays ofscanning beams in the sub-scanning section when the inclination of theincoming beams incident on the deflection plane of the light deflectoris small with respect to the deflection plane defined in thesub-scanning section and the deterioration in the imaging performancecaused by the conical scan is negligible. A similar effect as in thisexemplary embodiment can also be achieved by only curving the generatrixof one lens surface of the toric lens 8 in the sub-scanning direction.

Furthermore, in this exemplary embodiment, the toric lens 8 issymmetrical with respect to the optical axis of the imaging opticalsystem in the main scanning section since the incoming beams areincident on the light deflector from the center of the deflection angleof the deflection plane (frontal incidence). However, at least oneexemplary embodiment is not limited to this, and the toric lens 8 can beasymmetrical with respect to the optical axis of the imaging opticalsystem in the main scanning section.

Moreover, in this exemplary embodiment, the F-number (Fno) of theincident system in the main scanning direction is 7 and the F-number ofthe incident system in the sub-scanning direction is 6.4, andaccordingly, the F-number of the incident system in the sub-scanningdirection is larger (i.e., brighter) than that in the main scanningdirection. Thus, the incident optical system 5 includes the cylindricallens 2 and the spherical lens 4 in this order from the light-source unit1 such that the length of the optical path is reduced. However, at leastone exemplary embodiment is not limited to this, and, for example, thespherical lens 4 and the cylindrical lens 2 can be disposed in thisorder from the light-source unit 1 in the optical path.

Moreover, in this exemplary embodiment, the incident optical system 5 isan OFS. However, at least one exemplary embodiment is not limited tothis, and, for example, the incident optical system 5 of an underfilledoptical system (UFS) can produce a similar effect as in the firstexemplary embodiment. Furthermore, in this exemplary embodiment, thelight beams incident on the light deflector 6 slightly converge.However, at least one exemplary embodiment is not limited to this, and,for example, light beams that are parallel or slightly diverge can beused to produce a similar effect as in the first exemplary embodiment.

Moreover, in this exemplary embodiment, the imaging optical system 18 isof a single-path type. However, at least one exemplary embodiment is notlimited to this, and, for example, the imaging optical system 18 can beof a double-path type. Furthermore, in this exemplary embodiment, theimaging optical system 18 includes only one lens. However, at least oneexemplary embodiment is not limited to this, and, for example, theimaging optical system 18 can include a plurality of lenses. Inaddition, the imaging optical system 18 can include a curved mirror or adiffraction optical element. The single-path system herein means anoptical system where the scanning beams deflected from the deflectionplane 6 a of the light deflector 6 and reaching the surface to bescanned pass through the toric lens 8 of the imaging optical system 18.The double-path system herein means an optical system where both of thescanning beams deflected from the deflection plane 6 a of the lightdeflector 6 and reaching the a surface to be scanned and the incomingbeams incident on the deflection plane 6 a of the light deflector 6 passthrough the toric lens 8 of the imaging optical system 18.

Moreover, in this exemplary embodiment, the light beams incident on thedeflection plane 6 a of the light deflector 6 enter the deflection plane6 a from the center of the deflection angle of the deflection plane inthe main scanning section (frontal incidence). That is to say, the lightbeams incident on the deflection plane 6 a of the light deflector 6enter the deflection plane 6 a along the optical-axis direction of theimaging optical system. However, at least one exemplary embodiment isnot limited to this, and, for example, the light beams incident on thedeflection plane 6 a of the light deflector 6 can obliquely enter thedeflection plane 6 a in the main scanning section.

Moreover, in this exemplary embodiment, both the surfaces of the toriclens 8 are non-arc shaped with respect to the main scanning directionsuch that the fθ characteristic can be obtained by using only one toriclens. However, at least one exemplary embodiment is not limited to this,and, for example, arc-shaped surfaces of the toric lens with respect tothe main scanning direction can also produce a similar effect as in thefirst exemplary embodiment. Furthermore, in this exemplary embodiment,the toric lens 8 can be made of various materials (e.g., glass, resin,and other lens materials as known by one of ordinary skill in therelevant arts).

Next, the configuration of the optical scanning apparatus according tothis exemplary embodiment will be shown in Table 1. Curvature radii R,intervals D, and refractive indexes N of the scanning optical systemaccording to this exemplary embodiment will be shown in Table 2. Theaspherical shape of the toric lens (fθ lens) 8 according to thisexemplary embodiment will be shown in Table 3.

TABLE 1 Configuration in the first exemplary embodiment Laser power E 5mW Number of luminous points N 2 — Interval of luminous points d1 90 μmWavelength of use λ 780 nm Incident F-number in main scanning directionFm 7 — Incident F-number in sub-scanning direction Fs 6.4 — Width ofdeflection plane in main scanning direction W 2.83 mm Width of effectivelight beams in main scanning direction Wo 5.06 mm Circumscribed circlediameter of polygon φ1 7.4 mm Inscribed circle diameter of polygon φ26.84 mm Inclination of incident beams in sub-scanning direction θ 3 deg.Number of deflection planes M 8 — Scanning efficiency Du 90 % Maximumscanning angle ±α 40.5 deg. Magnification of imaging optical system insub-scanning direction Bs 2 times Effective scanning width 2Yo 214 mmSpot diameter in main scanning direction Pm 60 μm Spot diameter in sub-scanning direction Ps 70 μm

TABLE 2 Specification of scanning optical system in the first exemplaryembodiment Surface R D N LD 1st — 5.29 1 Cylinder 2nd ∞ 5 1.762 3rdTable 3 32.80 1 Spherical lens 4th ∞ 5 1.762 5th −29.86 66.97 1 POLY 6th∞ 44.45 1 fθ lens 7th Table 3 10.7 1.522 8th Table 3 119.47 1 Surface tobe scanned 9th ∞ — —

TABLE 3 Aspherical shape of imaging optical system in the firstexemplary embodiment Cylinder fθ lens 3rd 7th 8th Generatrix R ∞ 7.7956E+01  1.6946E+02 K 0 −7.2950E+00 −2.1925E+00 B4 0 −1.8300E−06−2.6462E−06 B6 0  7.0718E−10  7.2982E−10 B8 0 −1.4905E−13 −1.4716E−13B10 0  1.5955E−17  1.7906E−17 Meridian R −7.33E+00 −1.781E+01 −1.124E+01D2 0  1.289E−03  4.824E−04 D4 0  6.317E−07 −9.092E−08 D6 0  9.189E−11 2.427E−11 D8 0 −8.188E−15  6.829E−15 D10 0  7.301E−17 −2.906E−18Curvature of A0 — — 0 generatrix A2 — — 0 A4 — — 0 A6 — —  2.89E−12

The aspherical shape of the first lens surface R1 of the toric lens 8 isdefined by the following expressions.

When the point of intersection of the optical axis and the first lenssurface R1 is defined as the origin, an axis along the optical-axisdirection is defined asas the X axis, an axis orthogonal to the opticalaxis in the main scanning section is defined as the Y axis, and an axisorthogonal to the optical axis in the sub-scanning section is defined asthe Z axis; a generatrix can be defined as a line on the first lenssurface R1 of the toric lens 8 where the first lens surface R1 is cut bythe X-Y plane, and meridians can be defined as lines on the first lenssurface R1 of the toric lens 8 where the first lens surface R1 is cut bycutting planes parallel to the Z axis, each plane including a linenormal to the curved surface at the position Z=0. At this time, theshape of the generatrix is represented by Expression 1.

$\begin{matrix}{{Expression}\mspace{14mu} 1\text{:}} & \; \\{X = {\frac{Y^{2}/R}{1 + \sqrt{( {1 - {( {1 + K} ) \times ( {Y/R} )^{2}}} }} + {B_{4}{Y^{4}++}B_{6}Y^{6}} + {B_{8}Y^{8}} + {B_{10}Y^{10}}}} & (1)\end{matrix}$

Where, R indicates a curvature radius, and K, B₄, B₆, B₈, and B₁₀indicate aspherical coefficients of the generatrix.

The shape of the meridian is represented by Expression 2.

$\begin{matrix}{{Expression}\mspace{14mu} 2\text{:}} & \; \\{S = \frac{Z^{2}/r^{\prime}}{1 + \sqrt{( {1 - ( {Z/r^{\prime}} )^{2}} }}} & (2)\end{matrix}$

At this time, a curvature radius r′, which varies as a function of thevalue of Y, is represented by Expression 3.

$\begin{matrix}{{Expression}\mspace{14mu} 3\text{:}} & \; \\{r^{\prime} = {r_{0} \times ( {1 + {D_{2}Y^{2}} + {D_{4}Y^{4}} + {D_{6}Y^{6}} + {D_{8}Y^{8}} + {D_{10}Y^{10}}} )}} & (3)\end{matrix}$

Where, S indicates a distance in the direction of a line normal to thecurved surface of the lens at Z=0 between a point on a meridian at aposition of Z=0 and another point on the meridian, r₀ indicates thecurvature radius of the meridian on the optical axis, and D₂, D₄, D₆,D₈, and D₁₀ are coefficients.

FIG. 6 illustrates the shape of the second lens surface (toric surface)R2 of the toric lens (fθ lens) 8. The shape of the generatrix of thesecond lens surface R2 is represented by Expression 1, and the shape ofthe meridian is represented by Expressions 2 and 3 as in the case of thefirst lens surface R1. Moreover, in the schematic view, the optical axisof the toric lens corresponds to the X axis, and the main scanningdirection is along the Y axis. The generatrix is formed by connectingthe vertexes of the meridians, and the Z-axis component of thegeneratrix is represented by the following expression as a polynomial ofthe Y coordinate:Z=ΣAiYi (i=0, 1, 2, . . . )At this time, meridians can be defined as lines on the second lenssurface R2 of the toric lens 8 where the second lens surface R2 is cutby cutting planes parallel to the Z axis, each plane including a linenormal to the curved surface at the position Z=0 when the point ofintersection of the optical axis and the second lens surface R2 can bedefined as the origin, the axis along the optical-axis direction can bedefined as the X axis, the axis orthogonal to the optical axis in themain scanning section can be defined as the Y axis, and the axisorthogonal to the optical axis in the sub-scanning section can bedefined as the Z axis. In this exemplary embodiment, the Z-axiscomponent is represented by a sixth-degree polynomial. This expressionrepresents the degree of the curvature of the generatrix in thesub-scanning direction projected to the Y-Z plane, and corresponds toFIG. 6 described above.[Image-Forming Apparatus]

FIG. 7 is a sub-scanning section of principal parts of an image-formingapparatus according to an exemplary embodiment of the present invention.In the drawing, an image-forming apparatus 104 receives code data Dcinput by an external apparatus 117 such as a personal computer. The codedata Dc is converted into image data (dot data) Di by a printercontroller 111 in the apparatus. The image data Di is input to alight-scanning unit 100, which can have the structure described in thefirst exemplary embodiment. The light-scanning unit 100 emits lightbeams 103 modulated on the basis of the image data Di, and the lightbeams 103 scan a photosensitive surface of a photosensitive drum 101 inthe main scanning section.

The photosensitive drum 101 serving as a carrier of electrostatic latentimages (photoconductor) is rotated by a motor 115 in the clockwisedirection. With this rotation, the photosensitive surface of thephotosensitive drum 101 moves with respect to the light beams 103 in thesub-scanning section orthogonal to the main scanning section. Anelectrifying roller 102 for uniformly charging the surface of thephotosensitive drum 101 is disposed at an upper position of thephotosensitive drum 101 so as to be in contact with the surface. Thelight beams 103 emitted by the light-scanning unit 100 are incident onthe surface of the photosensitive drum 101 charged by the electrifyingroller 102.

As described above, the light beams 103 are modulated on the basis ofthe image data Di, and the irradiation of the light beams 103 forms theelectrostatic latent images on the surface of the photosensitive drum101. The electrostatic latent images are developed as toner images by adeveloping unit 107 disposed further downstream of the rotationdirection of the photosensitive drum 101 than the irradiation positionof the light beams 103 so as to be in contact with the photosensitivedrum 101.

The toner images developed by the developing unit 107 are transferred toa paper sheet 112 serving as a recording material by a transferringroller 108 disposed at a lower position of the photosensitive drum 101so as to face the photosensitive drum 101. The paper sheet 112 isaccommodated in a sheet cassette 109 disposed in the anterior position(right side in FIG. 7) of the photosensitive drum 101, but manual paperfeed is also available. A paper-feeding roller 110 is disposed at an endof the sheet cassette 109 so as to feed the paper sheet 112 in the sheetcassette 109 to a feeding route.

The paper sheet 112 to which the unfixed toner images are transferred isthen fed to a fixing unit disposed in the posterior position (left sidein FIG. 7) of the photosensitive drum 101. The fixing unit includes afixing roller 113, which can have a fixing heater (not shown) thereinand a pressurizing roller 114 pressed into contact with the fixingroller 113. The paper sheet 112 fed from the transferring unit is heatedwhile being pressurized between the fixing roller 113 and a pressurizingpart of the pressurizing roller 114, and thus the toner images are fixedon the paper sheet 112. Furthermore, a paper-ejecting roller 116 isdisposed in the posterior of the fixing roller 113 such that the papersheet 112 on which the toner images are fixed is ejected from theimage-forming apparatus.

Although not shown in FIG. 7, the printer controller 111 not onlyconverts the data as described above, but also controls componentsinside the image-forming apparatus such as the motor 115, and a polygonmotor in a scanning unit described below.

The recording density of the image-forming apparatus used in at leastone exemplary embodiment is not particularly limited. However, thestructure according to the first exemplary embodiment of at least oneexemplary embodiment is more effective in image-forming apparatuses of1200 dpi or higher resolution since higher resolution is required as therecording density becomes higher.

[Color-Image Forming Apparatus]

FIG. 8 is a schematic view of principal parts of a color-image formingapparatus according to an exemplary embodiment of the present invention.The color-image forming apparatus according to this exemplary embodimentis of a tandem type that has four optical scanning apparatuses disposedparallel to each other each recording image information on a surface ofa respective photosensitive drum serving as a carrier of images. FIG. 8shows a color-image forming apparatus 60, optical scanning apparatuses11, 12, 13, and 14 each, which can have the structure according to thefirst exemplary embodiment, photosensitive drums 21, 22, 23, and 24 eachserving as a carrier of images, developing units 31, 32, 33, and 34, anda feeding belt 51.

In FIG. 8, the color-image forming apparatus 60 receives color signalsof red (R), green (G), and blue (B) input by an external apparatus 52such as a personal computer. These color signals are converted intoimage data (dot data) of cyan (C), magenta (M), yellow (Y), and black(K) by a printer controller 53 in the apparatus. Pieces of the imagedata are input to the respective optical scanning apparatuses 11, 12,13, and 14. These optical scanning apparatuses 11, 12, 13, and 14 emitlight beams 41, 42, 43, and 44, respectively, modulated on the basis ofthe image data, and the light beams 41, 42, 43, and 44 each scan aphotosensitive surface of the respective photosensitive drums 21, 22,23, and 24 in the main scanning section.

The color-image forming apparatus according to this exemplary embodimentincludes the four aligned optical scanning apparatuses 11, 12, 13, and14 corresponding to the colors of C, M, Y, and K, respectively. Theoptical scanning apparatuses 11, 12, 13, and 14 record image signals(image information) on the surfaces of the photosensitive drums 21, 22,23, and 24 in tandem with each other. In this manner, color images areprinted at high speed.

As described above, the color-image forming apparatus according to thisexemplary embodiment forms the latent images of four colors on thesurfaces of the respective photosensitive drums 21, 22, 23, and 24 byusing the four optical scanning apparatuses 11, 12, 13, and 14 with thelight beams formed on the basis of the image data of four colors.Subsequently, the latent images are transferred to a recording materialso as to be overlapped, and thus a full-color image is formed.

A color-image reading apparatus including a charge-coupled device (CCD)sensor, for example, can be used as the external apparatus 52. In thiscase, the color-image reading apparatus and the color-image formingapparatus 60 form a color digital copier.

While the present invention has been described with reference toexemplary embodiments, it is to be understood that the invention is notlimited to the disclosed exemplary embodiments. The scope of thefollowing claims is to be accorded the broadest interpretation so as toencompass all modifications, equivalent structures and functions.

1. An optical scanning apparatus comprising: a light-source unit; anincident optical system for directing light beams emitted from thelight-source unit to a deflecting unit; and an imaging optical systemfor guiding the light beams deflected from the deflecting unit to asurface to be scanned, wherein the direction of the light beams emittedfrom the light-source unit and entering a deflection plane of thedeflecting unit is inclined with respect to the deflection plane in thesub-scanning section, and wherein the imaging optical system comprises atoric lens whose power in the main scanning direction is different fromthat in the sub-scanning direction; and in which the toric lens has afirst toric surface and a second toric surface, the curvature centers ofthe meridians of the first toric surface of the toric lens connected toform a curved line are located in a common plane Ha, the curvaturecenters of the meridians of the second toric surface connected to form acurved line are not located in a common plane, the generatrix of thesecond toric surface of the toric lens formed by connecting the vertexesof the meridians in every area of the second toric surface is curved inthe sub-scanning direction, and the degree of curvature ΔA of ageneratrix of the second toric surface satisfies the followingconditions:0 ≦ΔA ≦1 (mm)ΔA =|Zmax −Zmin|(mm), where Zmax and Zmin indicate the maximum value andthe minimum value, respectively, of the central positions of thecurvature radii of the meridians of the second toric surface in the Zdirection when the point of intersection of the optical axis of thesecond toric surface and the curved surface of the lens is defined asthe origin, and an axis orthogonal to the optical axis in thesub-scanning section is defined as the Z axis, and the curvature radii Rof the meridians of the second toric surface, over the entire area ofthe lens of use, are in the following range:22 mm<R<-11 mm.
 2. The optical scanning apparatus according to claim 1,wherein the curvature radii of the meridians of the first toric surfaceof the toric lens vary in magnitude from the optical axis of the imagingoptical system toward the periphery.
 3. The optical scanning apparatusaccording to claim 1, wherein the imaging optical system comprises asingle toric lens.
 4. The optical scanning apparatus according to claim1, wherein the curvature radii of the meridians of both the first toricsurface and the second toric surface of the toric lens vary in magnitudefrom the optical axis of the imaging optical system toward theperiphery.
 5. An image-forming apparatus comprising: the opticalscanning apparatus according to claim 1; a photosensitive memberdisposed on a surface to be scanned; a developing unit for developingelectrostatic latent images on the photosensitive member as tonerimages, the electrostatic latent images being formed by the light beamsthat are emitted by the optical scanning apparatus and scan thephotosensitive member; a transferring unit for transferring thedeveloped toner images to a recording material; and a fixing unit forfixing the transferred toner images on the recording material.
 6. Animage-forming apparatus comprising: the optical scanning apparatusaccording to claim 1; and a printer controller convening code data inputby an external apparatus into image signals and sending the signals tothe optical scanning apparatus.